1. Field of the Invention
The present invention relates to data storage devices and, more particularly, to identifying, isolating and reducing noise sources therein.
2. Description of the Related Art
Modern data storage devices (e.g., magnetic or optical disk or tape drives) are sophisticated devices having many possible sources of error signal noise sources. As data storage densities increase, it is becoming increasingly difficult to measure noise generated by these sources. Yet these measurements are important to make because they can be used to rank the noise sources and thereby prioritize design areas that would be most fruitful in the quest to design new generations of even greater density storage devices.
In general, dynamic system measurements can be performed in both time and frequency domains. Frequency domain measurements have proven to be particularly suited to this task.
There is a considerable literature describing making frequency domain measurements of dynamic systems. Good reference texts include: J. S. Bendat and A. G. Piersol, Random Data: Analysis and Measurement Procedures, New York, N.Y., John Wiley & Sons, second ed., 1986; A. V. Oppenheim and R. W. Schafer, Digital Signal Processing, Englewood Cliffs, N.J., Prentice Hall, 1970 (pages 532-574); L. Ljung, System Identification: Theory for the User, Prentice-Hall Information and System Sciences Series, Englewood Cliffs, N.J. 07632, Prentice-Hall, 1987 (pages 141-168); and G. F. Franklin, J. D. Powell, and M. L. Workman, Digital Control of Dynamic Systems, Menlo Park, Calif., Addison-Wesley, second ed., 1990 (pages 353-366, 805-816); as well as papers by P. L. Lin and Y. C. Wu, "Identification of Multi-input Multi Output Linear Systems from Frequency Response Data," Transactions of the ASME: Journal of Dynamic Systems, Measurements and Control, vol. 104, pp. 58-64, March 1982. The techniques are common enough so that they are in various products including instruments made by such companies as Hewlett-Packard (see, R. C. Blackham, J. A. Vasil, E. S. Atkinson, and R. W. Potter, "Measurement Modes and Digital Demodulation for a Low-frequency Analyzer," Hewlett-Packard Journal, vol. 38, pp. 17-25, January 1987; J. S. Epstein, G. R. Engel, D. R. Hiller, J. Glen L. Purdy, B. C. Hoog, and E. J. Wicklund, "Hardware Design for a Dynamic Signal Analyzer," Hewlett-Packard Journal, vol. 35, pp. 12-17, December 1984; Hewlett-Packard, Control System Development Using Dynamic Signal Analyzers: Application Note 243-2, 1984; Hewlett-Packard, HP 3563A Control Systems Analyzer, 1990; and Bruel & Kjaer, Multichannel Analysis System Type 3550, 1991) and software packages such as Matlab from the Mathworks (see L. Ljung, System Identification Toolbox for Use with Matlab, The Mathworks, Inc., 24 Prime Park Way, Natick, Mass. 01760, May 1995, 3rd Printing) or C-code included with textbooks such as P. M. Embree, C Algorithms for Real-Time DSP, Upper Saddle River, N.J. 07458, Prentice Hall PTR, 1995 (pages 186-193).
Furthermore, the filtering of stochastic processes is a well known art in both the fields of control and signal processing. This understanding forms the basis for all of the techniques which minimize the mean squared error of signals. It is commonly found in software such as Matlab from the Mathworks (see The Mathworks, Inc., 24 Prime Park Way, Natick, Mass. 01760, Matlab: Signal Processing Toolbox Users Guide, version 4 ed., December 1996 (pages 3-5-3-24) and such textbooks as M. S. Grewal and A. P. Andrews, Kalman Filtering: Theory and Practice, Prentice Hall Information and System Sciences Series, Englewood Cliffs, N.J. 07632, Prentice Hall, 1993 (pages 55-105). Some useful tutorials on these very simple concepts are in W. A. Gardner, Introduction to Random Processes with Applications to Signals and Systems, New York, N.Y., MacMillan Publishing Company, 1986 (pages 198-226 and 260-279) and in J. S. Bendat and A. G. Piersol, Random Data: Analysis and Measurement Procedures, New York, N.Y., John Wiley & Sons, second ed., 1986 (pages 56-105).
To briefly summarize, much of the useful work done in filtering makes use of special properties of Gaussian random processes. They have the property that if a signal, x, is filtered by a linear system, H, as shown in FIG. 2, then the output, y is also a Gaussian random process. If the process also has a property known as stationarity, then the Fourier Transform of the processes autocorrelation function exists. This is critical for filtering analyses because, in the Fourier transform domain, the Power Spectral Density (PSD) of y is given by EQU S.sub.y =.vertline.H.vertline..sup.2 S.sub.x ( 1)
The fact that one PSD can be obtained by filtering another PSD through some magnitude squared filter becomes invaluable for noise analysis, because noises can often be characterized and measured in terms of their PSDs. See, W. A. Gardner, Introduction to Random Processes with Applications to Signals and Systems, New York, N.Y., MacMillan Publishing Company, 1986; J. S. Bendat and A. G. Piersol, Random Data: Analysis and Measurement Procedures, New York, N.Y., John Wiley & Sons, second ed., 1986.
Bode's Integral Theorem (W. Bode, Network Analysis and Feedback Amplifier Design New York, Van Nostrand, 1945) is known to the art of electronic circuits and to the art of feedback control. The rest of the analysis of noise signals in storage devices is largely ad hoc. Also, as most of these signal processing algorithms are more concerned with optimizing a loop given a certain amount of noise than in actually decomposing the noise sources, there is no literature on a systematic method for the latter.
What is missing in the prior art is a unification of all these concepts, that takes the measurement process, the filtering process, and the understanding of Bode's Integral Theorem to yield a unified method of decomposing noise sources in a feedback control loop.
Thus, it can be seen that inadequate noise measurement techniques impose data storage density limits upon data storage devices, and hinder the use of these devices in many applications.
Therefore, there is an unresolved need for a noise measurement technique that can improve the design of data storage devices by identifying sources of noise within a device, and hence identify design areas to emphasize to increase storage density.